Solve =-5/2:(-sqrt{2})

$$= \frac { - 5 } { 2 } : ( - \sqrt { 2 } )$$

Evaluate

$$\frac{5\sqrt{2}}{4}\approx 1.767766953$$

Solution Steps

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{-\frac{5}{2}}{-\sqrt{2}}$$

Express \frac{-\frac{5}{2}}{-\sqrt{2}} as a single fraction.

$$\frac{-5}{2\left(-\sqrt{2}\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-5}{-2\sqrt{2}}$$

Rationalize the denominator of \frac{-5}{-2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-5\sqrt{2}}{-2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-5\sqrt{2}}{-2\times 2}$$

Multiply -2 and 2 to get -4.

$$\frac{-5\sqrt{2}}{-4}$$